Why is this really even a question? Do you see the original Xbox, NES, SNES, N64, GameCube, or PS1 (PS2 is a special exception) being sold in stores any more? Most people end up buying the new hardware and abandoning the old once the new, shinier console comes out.

Besides, the only thing most people used the PSP for anyhow was hacking it and putting emulators on it.

I believe that the Vita has gotten people interested in the PSP. If you look back you don't remember seeing many comercials for the PSP. Since the Vita came out people have seen that Playstation has hand held devices and know a little about them. I personally loved my PSP and I love my Vita. What got me hooked on the PSP was Final Fantasy Crisis Core. Certian titles are helping the PSP out and there are others that are benifiting the Vita. I think they majorly underplayed the Vita here though. However I think once the PS4 comes out the Vita will be a key player on that field as well, just like how the PSP could have been a key player with the PS3 if they thought to work through a few things.

I can't speak for anyone else but I can speak for myself; I don't play the PSP "anymore" for two major reasons...

Number One: No support. The PSP's collection of games wasn't small by any means but there weren't many stand-out titles. I feel like a majority were either remakes of older games or sequels to games released on other platforms. That said, I was able to find some hidden gems but those alone weren't enough to keep me playing.

Number Two: The Vita is out. If you are confused as to why that would make any difference, think of the Vita as the Gameboy Color and the PSP as the original Gameboy. The original made way for the Color because the Color had new features which developers could use to make better games. Now apply the same logic to the PSP and the Vita. I, as a consumer, have no reason to play the PSP when there are better games being made elsewhere.